The structures of the ferroelectric two-layer Aurivillius phases Bi ₂ ANb ₂ O ₉ (A=Ba, Sr, Ca) have been refined using a combination of X-ray and neutron powder diffraction data. Bi ₂ BaNb ₂ O ₉ is not significantly distorted from idealised symmetry and has been refined in tetragonal space group I4/mmm, a=3.9362(1) and c=25.6582(7) Å. The Sr and Ca compounds have been refined in orthorhombic space group A2 ₁ am, with a=5.5193(3), b=5.5148(3), c=25.0857(6) Å and a=5.4833(1), b=5.4423(1), c=24.8984(6) Å, respectively. The orthorhombic distortion increases with decreasing A ²⁺ cation size and originates from bonding requirements at the perovskite A site, in agreement with previous work. However, in contrast to earlier work, we find a partial mixing of Bi and A cations on their respective sites, which increases in the order Ca<Sr<Ba. This effect is also discussed in terms of bonding requirements at the metal sites and bond valence sum analysis. The combined use of X-ray and neutron powder diffraction data is found to be essential in determining this subtle effect, which may have important consequences in the interpretation of the ferroelectric behaviour of this family of materials.